Abstract

We demonstrate a method to simultaneously measure the rotational temperature and pump intensity in laser-induced molecular alignment by the time-resolved high harmonic spectroscopy (HHS). It relies on the sensitive dependence of the arising times of the local minima and maxima of the harmonic yields at the rotational revivals on the pump intensity and rotational temperature. By measuring the arising times of these local extrema from the time-resolved harmonic signals, the rotational temperature and pump intensity can be accurately measured. We have demonstrated our method using N2 molecules. The validity and robustness of our method are tested with different harmonic orders and by changing the gas pressures as well as the distance between the gas exit and the optical axis. Moreover, we have also demonstrated the versatility of our method by applying it to CO2 molecules.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (3)

E. Karamatskos, S. Raabe, T. Mullins, A. Trabattoni, P. Stammer, G. Goldsztejn, R. Johansen, K. Długołecki, H. Stapelfeldt, M. J. J. Vrakking, S. Trippel, A. Rouzée, and J. Küpper, “Molecular movie of ultrafast coherent rotational dynamics of OCS,” Nat. Commun. 10(1), 3364 (2019).
[Crossref]

Y. He, L. He, P. Lan, B. Wang, L. Li, X. Zhu, W. Cao, and P. Lu, “Direct imaging of molecular rotation with high-order-harmonic generation,” Phys. Rev. A 99(5), 053419 (2019).
[Crossref]

B. Wang, L. He, Y. He, Y. Zhang, R. Shao, P. Lan, and P. Lu, “All-optical measurement of high-order fractional molecular echoes by high-order harmonic generation,” Opt. Express 27(21), 30172–30181 (2019).
[Crossref]

2018 (3)

K. Lin, I. Tutunnikov, J. Qiang, J. Ma, Q. Song, Q. Ji, W. Zhang, H. Li, F. Sun, X. Gong, H. Li, P. Lu, H. Zeng, Y. Prior, I. S. Averbukh, and J. Wu, “All-optical field-free three-dimensional orientation of asymmetric-top molecules,” Nat. Commun. 9(1), 5134 (2018).
[Crossref]

C. Zhai, X. Zhang, X. Zhu, L. He, Y. Zhang, B. Wang, Q. Zhang, P. Lan, and P. Lu, “Single-shot molecular orbital tomography with orthogonal two-color fields,” Opt. Express 26(3), 2775–2784 (2018).
[Crossref]

L. He, P. Lan, A.-T. Le, B. Wang, B. Wang, X. Zhu, P. Lu, and C. D. Lin, “Real-time observation of molecular spinning with angular high-harmonic spectroscopy,” Phys. Rev. Lett. 121(16), 163201 (2018).
[Crossref]

2016 (1)

K. Lin, P. Lu, J. Ma, X. Gong, Q. Song, Q. Ji, W. Zhang, H. Zeng, J. Wu, G. Karras, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Echoes in space and time,” Phys. Rev. X 6(4), 041056 (2016).
[Crossref]

2015 (2)

K. Lin, Q. Song, X. Gong, Q. Ji, H. Pan, J. Ding, H. Zeng, and J. Wu, “Visualizing molecular unidirectional rotation,” Phys. Rev. A 92(1), 013410 (2015).
[Crossref]

P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350(6262), 790–795 (2015).
[Crossref]

2012 (2)

A. Rupenyan, J. B. Bertrand, D. M. Villeneuve, and H. J. Wörner, “All-optical measurement of high-harmonic amplitudes and phases in aligned molecules,” Phys. Rev. Lett. 108(3), 033903 (2012).
[Crossref]

S. Xu, X. Sun, B. Zeng, W. Chu, J. Zhao, W. Liu, Y. Cheng, Z. Xu, and S. L. Chin, “Simple method of measuring laser peak intensity inside femtosecond laser filament in air,” Opt. Express 20(1), 299–307 (2012).
[Crossref]

2011 (2)

C. Smeenk, J. Z. Salvail, L. Arissian, P. B. Corkum, C. T. Hebeisen, and A. Staudte, “Precise in-situ measurement of laser pulse intensity using strong field ionization,” Opt. Express 19(10), 9336–9344 (2011).
[Crossref]

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nat. Phys. 7(10), 822–826 (2011).
[Crossref]

2010 (2)

Y. Ohshima and H. Hasegawa, “Coherent rotational excitation by intense nonresonant laser fields,” Int. Rev. Phys. Chem. 29(4), 619–663 (2010).
[Crossref]

C. D. Lin, A.-T. Le, Z. Chen, T. Morishita, and R. Lucchese, “Strong-field rescattering physics—self-imaging of a molecule by its own electrons,” J. Phys. B: At., Mol. Opt. Phys. 43(12), 122001 (2010).
[Crossref]

2009 (7)

A.-T. Le, R. R. Lucchese, S. Tonzani, T. Morishita, and C. D. Lin, “Quantitative rescattering theory for high-order harmonic generation from molecules,” Phys. Rev. A 80(1), 013401 (2009).
[Crossref]

S. Fleischer, Y. Khodorkovsky, Y. Prior, and I. S. Averbukh, “Controlling the sense of molecular rotation,” New J. Phys. 11(10), 105039 (2009).
[Crossref]

A.-T. Le, R. R. Lucchese, and C. D. Lin, “Uncovering multiple orbitals influence in high harmonic generation from aligned N2,” J. Phys. B: At., Mol. Opt. Phys. 42(21), 211001 (2009).
[Crossref]

O. Ghafur, A. Rouzée, A. Gijsbertsen, W. K. Siu, S. Stolte, and M. J. J. Vrakking, “Impulsive orientation and alignment of quantum-state-selected NO molecules,” Nat. Phys. 5(4), 289–293 (2009).
[Crossref]

C. Z. Bisgaard, O. J. Clarkin, G. Wu, A. M. Lee, O. Geßner, C. C. Hayden, and A. Stolow, “Time-resolved molecular frame dynamics of fixed-in-space CS2 molecules,” Science 323(5920), 1464–1468 (2009).
[Crossref]

C. B. Madsen, L. B. Madsen, S. S. Viftrup, M. P. Johansson, T. B. Poulsen, L. Holmegaard, V. Kumarappan, K. A. Jørgensen, and H. Stapelfeldt, “Manipulating the torsion of molecules by strong laser pulses,” Phys. Rev. Lett. 102(7), 073007 (2009).
[Crossref]

K. Yoshii, G. Miyaji, and K. Miyazaki, “Measurement of molecular rotational temperature in a supersonic gas jet with high-order harmonic generation,” Opt. Lett. 34(11), 1651–1653 (2009).
[Crossref]

2008 (3)

J. Wu, H. Cai, H. Zeng, and A. Couairon, “Femtosecond filamentation and pulse compression in the wake of molecular alignment,” Opt. Lett. 33(22), 2593–2595 (2008).
[Crossref]

S. Saugout, E. Charron, and C. Cornaggia, “H2 double ionization with few-cycle laser pulses,” Phys. Rev. A 77(2), 023404 (2008).
[Crossref]

B. K. McFarland, J. P. Farrell, P. H. Bucksbaum, and M. Gühr, “High harmonic generation from multiple orbitals in N2,” Science 322(5905), 1232–1235 (2008).
[Crossref]

2007 (3)

V. Loriot, P. Tzallas, E. P. Benis, E. Hertz, B. Lavorel, D. Charalambidis, and O. Faucher, “Laser-induced field-free alignment of the OCS molecule,” J. Phys. B: At., Mol. Opt. Phys. 40(12), 2503–2510 (2007).
[Crossref]

T. Kanai, S. Minemoto, and H. Sakai, “Ellipticity dependence of high-order harmonic generation from aligned molecules,” Phys. Rev. Lett. 98(5), 053002 (2007).
[Crossref]

S. Ramakrishna and T. Seideman, “Information content of high harmonics generated from aligned molecules,” Phys. Rev. Lett. 99(11), 113901 (2007).
[Crossref]

2005 (2)

J. Itatani, D. Zeidler, J. Levesque, M. Spanner, D. M. Villeneuve, and P. B. Corkum, “Controlling high harmonic generation with molecular wave packets,” Phys. Rev. Lett. 94(12), 123902 (2005).
[Crossref]

K. Miyazaki, M. Kaku, G. Miyaji, A. Abdurrouf, and F. H. M. Faisal, “Field-free alignment of molecules observed with high-order harmonic generation,” Phys. Rev. Lett. 95(24), 243903 (2005).
[Crossref]

2004 (5)

A. S. Alnaser, X. M. Tong, T. Osipov, S. Voss, C. M. Maharjan, B. Shan, Z. Chang, and C. L. Cocke, “Laser-peak-intensity calibration using recoil-ion momentum imaging,” Phys. Rev. A 70(2), 023413 (2004).
[Crossref]

M. Kaku, K. Masuda, and K. Miyazaki, “Observation of revival structure in femtosecond-laser-induced alignment of N2 with high-order harmonic generation,” Jpn. J. Appl. Phys. 43(No. 4B), L591–L593 (2004).
[Crossref]

E. Péronne, M. D. Poulsen, H. Stapelfeldt, C. Z. Bisgaard, E. Hamilton, and T. Seideman, “Nonadiabatic laser-induced alignment of iodobenzene molecules,” Phys. Rev. A 70(6), 063410 (2004).
[Crossref]

T. Hornung, H. Skenderović, K.-L. Kompa, and M. Motzkus, “Prospect of temperature determination using degenerate four-wave mixing with sub-20 fs pulses,” J. Raman Spectrosc. 35(11), 934–938 (2004).
[Crossref]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[Crossref]

2003 (4)

I. V. Litvinyuk, K. F. Lee, P. W. Dooley, D. M. Rayner, D. M. Villeneuve, and P. B. Corkum, “Alignment-dependent strong field ionization of molecules,” Phys. Rev. Lett. 90(23), 233003 (2003).
[Crossref]

T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen, and H. Stapelfeldt, “Role of symmetry in strong-field ionization of molecules,” Phys. Rev. A 68(6), 063407 (2003).
[Crossref]

H. Stapelfeldt and T. Seideman, “Colloquium: Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75(2), 543–557 (2003).
[Crossref]

E. Péronne, M. D. Poulsen, C. Z. Bisgaard, H. Stapelfeldt, and T. Seideman, “Nonadiabatic alignment of asymmetric top molecules: Field-free alignment of iodobenzene,” Phys. Rev. Lett. 91(4), 043003 (2003).
[Crossref]

2002 (1)

N. Hay, R. Velotta, M. Lein, R. de Nalda, E. Heesel, M. Castillejo, and J. P. Marangos, “High-order harmonic generation in laser-aligned molecules,” Phys. Rev. A 65(5), 053805 (2002).
[Crossref]

2001 (4)

T. Lang, M. Motzkus, H. M. Frey, and P. Beaud, “High resolution femtosecond coherent anti-stokes raman scattering: Determination of rotational constants, molecular anharmonicity, collisional line shifts, and temperature,” J. Chem. Phys. 115(12), 5418–5426 (2001).
[Crossref]

L. Cai, J. Marango, and B. Friedrich, “Time-dependent alignment and orientation of molecules in combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 86(5), 775–778 (2001).
[Crossref]

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, “Phase modulation of ultrashort light pulses using molecular rotational wave packets,” Phys. Rev. Lett. 88(1), 013903 (2001).
[Crossref]

R. Velotta, N. Hay, M. B. Mason, M. Castillejo, and J. P. Marangos, “High-order harmonic generation in aligned molecules,” Phys. Rev. Lett. 87(18), 183901 (2001).
[Crossref]

1999 (1)

J. J. Larsen, I. Wendt-Larsen, and H. Stapelfeldt, “Controlling the branching ratio of photodissociation using aligned molecules,” Phys. Rev. Lett. 83(6), 1123–1126 (1999).
[Crossref]

1997 (1)

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[Crossref]

1991 (1)

H.-D. Barth, F. Huisken, and A. A. Ilyukhin, “Coherent raman spectroscopy of nitrogen molecules and clusters in supersonic jets,” Appl. Phys. B 52(2), 84–89 (1991).
[Crossref]

1990 (1)

H.-D. Barth and F. Huisken, “Investigation of librational motions in gas-phase CO2 clusters by coherent raman spectroscopy,” Chem. Phys. Lett. 169(3), 198–203 (1990).
[Crossref]

1988 (1)

H.-D. Barth, C. Jackschath, T. Pertsch, and F. Huisken, “CARS spectroscopy of molecules and clusters in supersonic jets,” Appl. Phys. B 45(4), 205–214 (1988).
[Crossref]

1986 (1)

F. Huisken and T. Pertsch, “Coherent anti-stokes raman spectroscopy (CARS) of the v3 band of methane in supersonic molecular beams,” Appl. Phys. B 41(3), 173–178 (1986).
[Crossref]

1981 (1)

1979 (1)

P. Huber-Wälchli, D. M. Guthals, and J. W. Nibler, “Cars spectra of supersonic molecular beams,” Chem. Phys. Lett. 67(2-3), 233–236 (1979).
[Crossref]

Abdurrouf, A.

K. Miyazaki, M. Kaku, G. Miyaji, A. Abdurrouf, and F. H. M. Faisal, “Field-free alignment of molecules observed with high-order harmonic generation,” Phys. Rev. Lett. 95(24), 243903 (2005).
[Crossref]

Alnaser, A. S.

A. S. Alnaser, X. M. Tong, T. Osipov, S. Voss, C. M. Maharjan, B. Shan, Z. Chang, and C. L. Cocke, “Laser-peak-intensity calibration using recoil-ion momentum imaging,” Phys. Rev. A 70(2), 023413 (2004).
[Crossref]

Arissian, L.

Averbukh, I. S.

K. Lin, I. Tutunnikov, J. Qiang, J. Ma, Q. Song, Q. Ji, W. Zhang, H. Li, F. Sun, X. Gong, H. Li, P. Lu, H. Zeng, Y. Prior, I. S. Averbukh, and J. Wu, “All-optical field-free three-dimensional orientation of asymmetric-top molecules,” Nat. Commun. 9(1), 5134 (2018).
[Crossref]

K. Lin, P. Lu, J. Ma, X. Gong, Q. Song, Q. Ji, W. Zhang, H. Zeng, J. Wu, G. Karras, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Echoes in space and time,” Phys. Rev. X 6(4), 041056 (2016).
[Crossref]

S. Fleischer, Y. Khodorkovsky, Y. Prior, and I. S. Averbukh, “Controlling the sense of molecular rotation,” New J. Phys. 11(10), 105039 (2009).
[Crossref]

Baertschy, M.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, “Phase modulation of ultrashort light pulses using molecular rotational wave packets,” Phys. Rev. Lett. 88(1), 013903 (2001).
[Crossref]

Bandrauk, A. D.

P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350(6262), 790–795 (2015).
[Crossref]

Bartels, R. A.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, “Phase modulation of ultrashort light pulses using molecular rotational wave packets,” Phys. Rev. Lett. 88(1), 013903 (2001).
[Crossref]

Barth, H.-D.

H.-D. Barth, F. Huisken, and A. A. Ilyukhin, “Coherent raman spectroscopy of nitrogen molecules and clusters in supersonic jets,” Appl. Phys. B 52(2), 84–89 (1991).
[Crossref]

H.-D. Barth and F. Huisken, “Investigation of librational motions in gas-phase CO2 clusters by coherent raman spectroscopy,” Chem. Phys. Lett. 169(3), 198–203 (1990).
[Crossref]

H.-D. Barth, C. Jackschath, T. Pertsch, and F. Huisken, “CARS spectroscopy of molecules and clusters in supersonic jets,” Appl. Phys. B 45(4), 205–214 (1988).
[Crossref]

Baykusheva, D.

P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350(6262), 790–795 (2015).
[Crossref]

Beaud, P.

T. Lang, M. Motzkus, H. M. Frey, and P. Beaud, “High resolution femtosecond coherent anti-stokes raman scattering: Determination of rotational constants, molecular anharmonicity, collisional line shifts, and temperature,” J. Chem. Phys. 115(12), 5418–5426 (2001).
[Crossref]

Benis, E. P.

V. Loriot, P. Tzallas, E. P. Benis, E. Hertz, B. Lavorel, D. Charalambidis, and O. Faucher, “Laser-induced field-free alignment of the OCS molecule,” J. Phys. B: At., Mol. Opt. Phys. 40(12), 2503–2510 (2007).
[Crossref]

Bertrand, J. B.

A. Rupenyan, J. B. Bertrand, D. M. Villeneuve, and H. J. Wörner, “All-optical measurement of high-harmonic amplitudes and phases in aligned molecules,” Phys. Rev. Lett. 108(3), 033903 (2012).
[Crossref]

Bisgaard, C. Z.

C. Z. Bisgaard, O. J. Clarkin, G. Wu, A. M. Lee, O. Geßner, C. C. Hayden, and A. Stolow, “Time-resolved molecular frame dynamics of fixed-in-space CS2 molecules,” Science 323(5920), 1464–1468 (2009).
[Crossref]

E. Péronne, M. D. Poulsen, H. Stapelfeldt, C. Z. Bisgaard, E. Hamilton, and T. Seideman, “Nonadiabatic laser-induced alignment of iodobenzene molecules,” Phys. Rev. A 70(6), 063410 (2004).
[Crossref]

E. Péronne, M. D. Poulsen, C. Z. Bisgaard, H. Stapelfeldt, and T. Seideman, “Nonadiabatic alignment of asymmetric top molecules: Field-free alignment of iodobenzene,” Phys. Rev. Lett. 91(4), 043003 (2003).
[Crossref]

T. K. Kjeldsen, C. Z. Bisgaard, L. B. Madsen, and H. Stapelfeldt, “Role of symmetry in strong-field ionization of molecules,” Phys. Rev. A 68(6), 063407 (2003).
[Crossref]

Bucksbaum, P. H.

B. K. McFarland, J. P. Farrell, P. H. Bucksbaum, and M. Gühr, “High harmonic generation from multiple orbitals in N2,” Science 322(5905), 1232–1235 (2008).
[Crossref]

Byer, R. L.

Cai, H.

Cai, L.

L. Cai, J. Marango, and B. Friedrich, “Time-dependent alignment and orientation of molecules in combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 86(5), 775–778 (2001).
[Crossref]

Calegari, F.

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nat. Phys. 7(10), 822–826 (2011).
[Crossref]

Cao, W.

Y. He, L. He, P. Lan, B. Wang, L. Li, X. Zhu, W. Cao, and P. Lu, “Direct imaging of molecular rotation with high-order-harmonic generation,” Phys. Rev. A 99(5), 053419 (2019).
[Crossref]

Castillejo, M.

N. Hay, R. Velotta, M. Lein, R. de Nalda, E. Heesel, M. Castillejo, and J. P. Marangos, “High-order harmonic generation in laser-aligned molecules,” Phys. Rev. A 65(5), 053805 (2002).
[Crossref]

R. Velotta, N. Hay, M. B. Mason, M. Castillejo, and J. P. Marangos, “High-order harmonic generation in aligned molecules,” Phys. Rev. Lett. 87(18), 183901 (2001).
[Crossref]

Chang, Z.

A. S. Alnaser, X. M. Tong, T. Osipov, S. Voss, C. M. Maharjan, B. Shan, Z. Chang, and C. L. Cocke, “Laser-peak-intensity calibration using recoil-ion momentum imaging,” Phys. Rev. A 70(2), 023413 (2004).
[Crossref]

Charalambidis, D.

V. Loriot, P. Tzallas, E. P. Benis, E. Hertz, B. Lavorel, D. Charalambidis, and O. Faucher, “Laser-induced field-free alignment of the OCS molecule,” J. Phys. B: At., Mol. Opt. Phys. 40(12), 2503–2510 (2007).
[Crossref]

Charron, E.

S. Saugout, E. Charron, and C. Cornaggia, “H2 double ionization with few-cycle laser pulses,” Phys. Rev. A 77(2), 023404 (2008).
[Crossref]

Chen, Z.

C. D. Lin, A.-T. Le, Z. Chen, T. Morishita, and R. Lucchese, “Strong-field rescattering physics—self-imaging of a molecule by its own electrons,” J. Phys. B: At., Mol. Opt. Phys. 43(12), 122001 (2010).
[Crossref]

Cheng, Y.

Chin, S. L.

Chu, W.

Clarkin, O. J.

C. Z. Bisgaard, O. J. Clarkin, G. Wu, A. M. Lee, O. Geßner, C. C. Hayden, and A. Stolow, “Time-resolved molecular frame dynamics of fixed-in-space CS2 molecules,” Science 323(5920), 1464–1468 (2009).
[Crossref]

Cocke, C. L.

A. S. Alnaser, X. M. Tong, T. Osipov, S. Voss, C. M. Maharjan, B. Shan, Z. Chang, and C. L. Cocke, “Laser-peak-intensity calibration using recoil-ion momentum imaging,” Phys. Rev. A 70(2), 023413 (2004).
[Crossref]

Corkum, P. B.

C. Smeenk, J. Z. Salvail, L. Arissian, P. B. Corkum, C. T. Hebeisen, and A. Staudte, “Precise in-situ measurement of laser pulse intensity using strong field ionization,” Opt. Express 19(10), 9336–9344 (2011).
[Crossref]

J. Itatani, D. Zeidler, J. Levesque, M. Spanner, D. M. Villeneuve, and P. B. Corkum, “Controlling high harmonic generation with molecular wave packets,” Phys. Rev. Lett. 94(12), 123902 (2005).
[Crossref]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[Crossref]

I. V. Litvinyuk, K. F. Lee, P. W. Dooley, D. M. Rayner, D. M. Villeneuve, and P. B. Corkum, “Alignment-dependent strong field ionization of molecules,” Phys. Rev. Lett. 90(23), 233003 (2003).
[Crossref]

Cornaggia, C.

S. Saugout, E. Charron, and C. Cornaggia, “H2 double ionization with few-cycle laser pulses,” Phys. Rev. A 77(2), 023404 (2008).
[Crossref]

Couairon, A.

de Nalda, R.

N. Hay, R. Velotta, M. Lein, R. de Nalda, E. Heesel, M. Castillejo, and J. P. Marangos, “High-order harmonic generation in laser-aligned molecules,” Phys. Rev. A 65(5), 053805 (2002).
[Crossref]

De Silvestri, S.

C. Vozzi, M. Negro, F. Calegari, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Generalized molecular orbital tomography,” Nat. Phys. 7(10), 822–826 (2011).
[Crossref]

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[Crossref]

Ding, J.

K. Lin, Q. Song, X. Gong, Q. Ji, H. Pan, J. Ding, H. Zeng, and J. Wu, “Visualizing molecular unidirectional rotation,” Phys. Rev. A 92(1), 013410 (2015).
[Crossref]

Dlugolecki, K.

E. Karamatskos, S. Raabe, T. Mullins, A. Trabattoni, P. Stammer, G. Goldsztejn, R. Johansen, K. Długołecki, H. Stapelfeldt, M. J. J. Vrakking, S. Trippel, A. Rouzée, and J. Küpper, “Molecular movie of ultrafast coherent rotational dynamics of OCS,” Nat. Commun. 10(1), 3364 (2019).
[Crossref]

Dooley, P. W.

I. V. Litvinyuk, K. F. Lee, P. W. Dooley, D. M. Rayner, D. M. Villeneuve, and P. B. Corkum, “Alignment-dependent strong field ionization of molecules,” Phys. Rev. Lett. 90(23), 233003 (2003).
[Crossref]

Duncan, M. D.

Faisal, F. H. M.

K. Miyazaki, M. Kaku, G. Miyaji, A. Abdurrouf, and F. H. M. Faisal, “Field-free alignment of molecules observed with high-order harmonic generation,” Phys. Rev. Lett. 95(24), 243903 (2005).
[Crossref]

Farrell, J. P.

B. K. McFarland, J. P. Farrell, P. H. Bucksbaum, and M. Gühr, “High harmonic generation from multiple orbitals in N2,” Science 322(5905), 1232–1235 (2008).
[Crossref]

Faucher, O.

K. Lin, P. Lu, J. Ma, X. Gong, Q. Song, Q. Ji, W. Zhang, H. Zeng, J. Wu, G. Karras, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Echoes in space and time,” Phys. Rev. X 6(4), 041056 (2016).
[Crossref]

V. Loriot, P. Tzallas, E. P. Benis, E. Hertz, B. Lavorel, D. Charalambidis, and O. Faucher, “Laser-induced field-free alignment of the OCS molecule,” J. Phys. B: At., Mol. Opt. Phys. 40(12), 2503–2510 (2007).
[Crossref]

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68(9), 3277–3295 (1997).
[Crossref]

Fleischer, S.

S. Fleischer, Y. Khodorkovsky, Y. Prior, and I. S. Averbukh, “Controlling the sense of molecular rotation,” New J. Phys. 11(10), 105039 (2009).
[Crossref]

Frey, H. M.

T. Lang, M. Motzkus, H. M. Frey, and P. Beaud, “High resolution femtosecond coherent anti-stokes raman scattering: Determination of rotational constants, molecular anharmonicity, collisional line shifts, and temperature,” J. Chem. Phys. 115(12), 5418–5426 (2001).
[Crossref]

Friedrich, B.

L. Cai, J. Marango, and B. Friedrich, “Time-dependent alignment and orientation of molecules in combined electrostatic and pulsed nonresonant laser fields,” Phys. Rev. Lett. 86(5), 775–778 (2001).
[Crossref]

Gershnabel, E.

K. Lin, P. Lu, J. Ma, X. Gong, Q. Song, Q. Ji, W. Zhang, H. Zeng, J. Wu, G. Karras, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Echoes in space and time,” Phys. Rev. X 6(4), 041056 (2016).
[Crossref]

Geßner, O.

C. Z. Bisgaard, O. J. Clarkin, G. Wu, A. M. Lee, O. Geßner, C. C. Hayden, and A. Stolow, “Time-resolved molecular frame dynamics of fixed-in-space CS2 molecules,” Science 323(5920), 1464–1468 (2009).
[Crossref]

Ghafur, O.

O. Ghafur, A. Rouzée, A. Gijsbertsen, W. K. Siu, S. Stolte, and M. J. J. Vrakking, “Impulsive orientation and alignment of quantum-state-selected NO molecules,” Nat. Phys. 5(4), 289–293 (2009).
[Crossref]

Gijsbertsen, A.

O. Ghafur, A. Rouzée, A. Gijsbertsen, W. K. Siu, S. Stolte, and M. J. J. Vrakking, “Impulsive orientation and alignment of quantum-state-selected NO molecules,” Nat. Phys. 5(4), 289–293 (2009).
[Crossref]

Goldsztejn, G.

E. Karamatskos, S. Raabe, T. Mullins, A. Trabattoni, P. Stammer, G. Goldsztejn, R. Johansen, K. Długołecki, H. Stapelfeldt, M. J. J. Vrakking, S. Trippel, A. Rouzée, and J. Küpper, “Molecular movie of ultrafast coherent rotational dynamics of OCS,” Nat. Commun. 10(1), 3364 (2019).
[Crossref]

Gong, X.

K. Lin, I. Tutunnikov, J. Qiang, J. Ma, Q. Song, Q. Ji, W. Zhang, H. Li, F. Sun, X. Gong, H. Li, P. Lu, H. Zeng, Y. Prior, I. S. Averbukh, and J. Wu, “All-optical field-free three-dimensional orientation of asymmetric-top molecules,” Nat. Commun. 9(1), 5134 (2018).
[Crossref]

K. Lin, P. Lu, J. Ma, X. Gong, Q. Song, Q. Ji, W. Zhang, H. Zeng, J. Wu, G. Karras, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Echoes in space and time,” Phys. Rev. X 6(4), 041056 (2016).
[Crossref]

K. Lin, Q. Song, X. Gong, Q. Ji, H. Pan, J. Ding, H. Zeng, and J. Wu, “Visualizing molecular unidirectional rotation,” Phys. Rev. A 92(1), 013410 (2015).
[Crossref]

Grassi, G.

P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350(6262), 790–795 (2015).
[Crossref]

Greene, C. H.

R. A. Bartels, T. C. Weinacht, N. Wagner, M. Baertschy, C. H. Greene, M. M. Murnane, and H. C. Kapteyn, “Phase modulation of ultrashort light pulses using molecular rotational wave packets,” Phys. Rev. Lett. 88(1), 013903 (2001).
[Crossref]

Gühr, M.

B. K. McFarland, J. P. Farrell, P. H. Bucksbaum, and M. Gühr, “High harmonic generation from multiple orbitals in N2,” Science 322(5905), 1232–1235 (2008).
[Crossref]

Guthals, D. M.

P. Huber-Wälchli, D. M. Guthals, and J. W. Nibler, “Cars spectra of supersonic molecular beams,” Chem. Phys. Lett. 67(2-3), 233–236 (1979).
[Crossref]

Hamilton, E.

E. Péronne, M. D. Poulsen, H. Stapelfeldt, C. Z. Bisgaard, E. Hamilton, and T. Seideman, “Nonadiabatic laser-induced alignment of iodobenzene molecules,” Phys. Rev. A 70(6), 063410 (2004).
[Crossref]

Hartmann, J.-M.

K. Lin, P. Lu, J. Ma, X. Gong, Q. Song, Q. Ji, W. Zhang, H. Zeng, J. Wu, G. Karras, G. Siour, J.-M. Hartmann, O. Faucher, E. Gershnabel, Y. Prior, and I. S. Averbukh, “Echoes in space and time,” Phys. Rev. X 6(4), 041056 (2016).
[Crossref]

Hasegawa, H.

Y. Ohshima and H. Hasegawa, “Coherent rotational excitation by intense nonresonant laser fields,” Int. Rev. Phys. Chem. 29(4), 619–663 (2010).
[Crossref]

Hay, N.

N. Hay, R. Velotta, M. Lein, R. de Nalda, E. Heesel, M. Castillejo, and J. P. Marangos, “High-order harmonic generation in laser-aligned molecules,” Phys. Rev. A 65(5), 053805 (2002).
[Crossref]

R. Velotta, N. Hay, M. B. Mason, M. Castillejo, and J. P. Marangos, “High-order harmonic generation in aligned molecules,” Phys. Rev. Lett. 87(18), 183901 (2001).
[Crossref]

Hayden, C. C.

C. Z. Bisgaard, O. J. Clarkin, G. Wu, A. M. Lee, O. Geßner, C. C. Hayden, and A. Stolow, “Time-resolved molecular frame dynamics of fixed-in-space CS2 molecules,” Science 323(5920), 1464–1468 (2009).
[Crossref]

He, L.

B. Wang, L. He, Y. He, Y. Zhang, R. Shao, P. Lan, and P. Lu, “All-optical measurement of high-order fractional molecular echoes by high-order harmonic generation,” Opt. Express 27(21), 30172–30181 (2019).
[Crossref]

Y. He, L. He, P. Lan, B. Wang, L. Li, X. Zhu, W. Cao, and P. Lu, “Direct imaging of molecular rotation with high-order-harmonic generation,” Phys. Rev. A 99(5), 053419 (2019).
[Crossref]

L. He, P. Lan, A.-T. Le, B. Wang, B. Wang, X. Zhu, P. Lu, and C. D. Lin, “Real-time observation of molecular spinning with angular high-harmonic spectroscopy,” Phys. Rev. Lett. 121(16), 163201 (2018).
[Crossref]

C. Zhai, X. Zhang, X. Zhu, L. He, Y. Zhang, B. Wang, Q. Zhang, P. Lan, and P. Lu, “Single-shot molecular orbital tomography with orthogonal two-color fields,” Opt. Express 26(3), 2775–2784 (2018).
[Crossref]

He, Y.

B. Wang, L. He, Y. He, Y. Zhang, R. Shao, P. Lan, and P. Lu, “All-optical measurement of high-order fractional molecular echoes by high-order harmonic generation,” Opt. Express 27(21), 30172–30181 (2019).
[Crossref]

Y. He, L. He, P. Lan, B. Wang, L. Li, X. Zhu, W. Cao, and P. Lu, “Direct imaging of molecular rotation with high-order-harmonic generation,” Phys. Rev. A 99(5), 053419 (2019).
[Crossref]

Hebeisen, C. T.

Heesel, E.

N. Hay, R. Velotta, M. Lein, R. de Nalda, E. Heesel, M. Castillejo, and J. P. Marangos, “High-order harmonic generation in laser-aligned molecules,” Phys. Rev. A 65(5), 053805 (2002).
[Crossref]

Hertz, E.

V. Loriot, P. Tzallas, E. P. Benis, E. Hertz, B. Lavorel, D. Charalambidis, and O. Faucher, “Laser-induced field-free alignment of the OCS molecule,” J. Phys. B: At., Mol. Opt. Phys. 40(12), 2503–2510 (2007).
[Crossref]

Holmegaard, L.

C. B. Madsen, L. B. Madsen, S. S. Viftrup, M. P. Johansson, T. B. Poulsen, L. Holmegaard, V. Kumarappan, K. A. Jørgensen, and H. Stapelfeldt, “Manipulating the torsion of molecules by strong laser pulses,” Phys. Rev. Lett. 102(7), 073007 (2009).
[Crossref]

Hornung, T.

T. Hornung, H. Skenderović, K.-L. Kompa, and M. Motzkus, “Prospect of temperature determination using degenerate four-wave mixing with sub-20 fs pulses,” J. Raman Spectrosc. 35(11), 934–938 (2004).
[Crossref]

Horný, L.

P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350(6262), 790–795 (2015).
[Crossref]

Huber-Wälchli, P.

P. Huber-Wälchli, D. M. Guthals, and J. W. Nibler, “Cars spectra of supersonic molecular beams,” Chem. Phys. Lett. 67(2-3), 233–236 (1979).
[Crossref]

Huisken, F.

H.-D. Barth, F. Huisken, and A. A. Ilyukhin, “Coherent raman spectroscopy of nitrogen molecules and clusters in supersonic jets,” Appl. Phys. B 52(2), 84–89 (1991).
[Crossref]

H.-D. Barth and F. Huisken, “Investigation of librational motions in gas-phase CO2 clusters by coherent raman spectroscopy,” Chem. Phys. Lett. 169(3), 198–203 (1990).
[Crossref]

H.-D. Barth, C. Jackschath, T. Pertsch, and F. Huisken, “CARS spectroscopy of molecules and clusters in supersonic jets,” Appl. Phys. B 45(4), 205–214 (1988).
[Crossref]

F. Huisken and T. Pertsch, “Coherent anti-stokes raman spectroscopy (CARS) of the v3 band of methane in supersonic molecular beams,” Appl. Phys. B 41(3), 173–178 (1986).
[Crossref]

Ilyukhin, A. A.

H.-D. Barth, F. Huisken, and A. A. Ilyukhin, “Coherent raman spectroscopy of nitrogen molecules and clusters in supersonic jets,” Appl. Phys. B 52(2), 84–89 (1991).
[Crossref]

Itatani, J.

J. Itatani, D. Zeidler, J. Levesque, M. Spanner, D. M. Villeneuve, and P. B. Corkum, “Controlling high harmonic generation with molecular wave packets,” Phys. Rev. Lett. 94(12), 123902 (2005).
[Crossref]

J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pépin, J. C. Kieffer, P. B. Corkum, and D. M. Villeneuve, “Tomographic imaging of molecular orbitals,” Nature 432(7019), 867–871 (2004).
[Crossref]

Jackschath, C.

H.-D. Barth, C. Jackschath, T. Pertsch, and F. Huisken, “CARS spectroscopy of molecules and clusters in supersonic jets,” Appl. Phys. B 45(4), 205–214 (1988).
[Crossref]

Jensen, F.

P. M. Kraus, B. Mignolet, D. Baykusheva, A. Rupenyan, L. Horný, E. F. Penka, G. Grassi, O. I. Tolstikhin, J. Schneider, F. Jensen, L. B. Madsen, A. D. Bandrauk, F. Remacle, and H. J. Wörner, “Measurement and laser control of attosecond charge migration in ionized iodoacetylene,” Science 350(6262), 790–795 (2015).
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Ji, Q.

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Figures (7)

Fig. 1.
Fig. 1. (a) Schematic diagram of the experimental setup. (b) Measured HHG signal of H21 (blue dots) from ${\textrm {N}_2}$ molecule as a function of the pump-probe time delay. The solid line is the fitting result. (c) Same as (b), but for theoretical result simulated with the rotational temperature of 100 K and the pump intensity of 3.5 $\times 10^{13}$ W/cm$^2$ . $t_a, t_b, t_c, t_d$ pointed out by arrows are four characteristic times, which are independent of the rotational temperature and the pump intensity. The dashed lines together with arrows on top indicate the arising times of local extrema of HHG yields at rotational revivals.
Fig. 2.
Fig. 2. (a) The arising time of the local maximum $t_{max}^{1/2}$ at $\tfrac {1}{2}$ $T_{rev}$ for ${\textrm {N}_2}$ molecule as a function of the rotational temperature and pump intensity. The black line is a contour line for $t_{max}^{1/2}=4.024$ ps. (b) Same as (a), but for the arising time of local minimum $t_{min}^{1/2}$ at $\tfrac {1}{2}$ $T_{rev}$. The red dotted line is a contour line for $t_{min}^{1/2}=4.388$ ps. (c) Contour lines for $t=4.024$ ps (solid line) and $t=4.388$ ps (dotted line). The intersection indicates the pending rotational temperature and pump intensity.
Fig. 3.
Fig. 3. The measured rotational temperature and pump intensity as a function of harmonic order. Here, the error bars of both results represent the standard deviation of five independent measurements.
Fig. 4.
Fig. 4. The measured rotational temperature and pump intensity as a function of pressure. Here, the error bars of both results represent the standard deviation of five independent measurements.
Fig. 5.
Fig. 5. The measured rotational temperature and pump intensity as a function of distance $x$. Here, the error bars of both results represent the standard deviation of five independent measurements.
Fig. 6.
Fig. 6. (a) Measured HHG signal of H25 (blue dots) from ${\textrm {CO}_2}$ molecule as a function of the pump-probe time delay. The solid line is the fitting result. The dashed lines together with arrows on top indicate the arising times of local extrema of HHG yields at rotational revivals. (b) The arising time of local minimum $t_{min}^{1/2}$ at $\tfrac {1}{2}$ $T_{rev}$ as a function of the rotational temperature and pump intensity. The black line is a contour line for $t_{min}^{1/2}=21.013$ ps. (c) Same as (b), but for the arising time of local maximum $t_{max}^{1/2}$ at $\tfrac {1}{2}$ $T_{rev}$. The red dotted line is a contour line for $t_{max}^{1/2}=21.791$ ps. (d) Contour lines for $t=21.013$ ps (solid line) and $t=21.791$ ps (dotted line). The intersection indicates the pending rotational temperature and pump intensity.
Fig. 7.
Fig. 7. (a) The arising time of the local minimum $t_{min}^{1/4}$ at $\tfrac {1}{4}$ $T_{rev}$ for ${\textrm {CO}_2}$ molecule as a function of the rotational temperature and pump intensity. The red dotted line is a contour line for $t_{min}^{1/4}=11.502$ ps. (b) Contour lines for $t=21.013$ ps (solid line) and $t=11.502$ ps (dotted line). The intersection indicates the pending rotational temperature and pump intensity.

Equations (3)

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i Ψ J M ( θ , ϕ , t ) t = [ B e J 2 1 4 ( α c o s 2 θ + α s i n 2 θ ) E ( t ) 2 ] Ψ J M ( θ , ϕ , t ) .
ρ ( θ , ϕ , t ) = J M Γ J M | Ψ J M ( θ , ϕ , t ) | 2 ,
I q ( t ) = | ϕ = 0 2 π θ = 0 π S q ( θ ) ρ ( θ , ϕ , t ) sin θ d θ d ϕ | 2 .

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